These are the ones from the TV show and movies.
NX-01 - NX class - served 2151 to 2161
NCC-1701 - Constitution class - served 2245 to 2285
NCC-1701-A - Constitution class (refit) - served 2286 to 2293
NCC-1701-B - Excelsior class (refit) - served 2293 to 2329
NCC-1701-C - Ambassador class - served 2332 to 2344
NCC-1701-D - Galaxy class - served 2363 to 2371
NCC-1701-D alternate timeline - Galaxy class (refit), aka Galaxy-X, aka Galaxy-dreadnought - served ? to ~2395
NCC-1701-E - Sovereign class - served 2372 to ?
NCC-1701-J - Universe class (possible/alternate future) - served 26th century